In the \(k_T\)  factorization approach (also named as high-energy factorization), one can parametrize the \(\gamma ^*p \rightarrow X\)  vertices in terms of the proton structure functions. The photons from inelastic production have transverse momenta and non-zero virtualities \(Q^2\)  and the unintegrated photon distributions are used, in contrast to collinear distributions.
In the DIS limit, the unintegrated inelastic photon flux can be obtained using the following equation [1]}, [2]}:
\(\gamma ^p_{inel}(x,Q^2) = {1\over x}{1 \over \pi Q^2} \, \int _{M^2_{\rm thr}} dM_X^2 {\cal {F}}^{\mathrm {in}}_{\gamma ^* \leftarrow p} (x,\vec{q}_T^2,M^2_X) \, ,\) 
